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On the Mode II Loading of Adhesive Joints
Fracture of Polymers, Composites and Adhesives II B.R.K. Blackman, A. Pavan and J.G. Williams (Eds) © 2003 Elsevier Ltd. and ESIS. All rights reserved.
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ON THE MODE II LOADING OF ADHESIVE JOINTS
B.R.K. BLACKMAN, AJ. KINLOCH & M. PARASCHI Department of Mechanical Engineering Imperial College London Exhibition Road London SW7 2BX. UK.
ABSTRACT This paper reports the results of research studies on measuring the mode II fracture toughness, Giic, of structural adhesive joints via a Linear Elastic Fracture Mechanics (LEFM) test method. Adhesive joints were manufactured using carbon-fibre reinforced plastic substrates and these were bonded with one of two commercial structural epoxy adhesives. Mode II loading was achieved using the end-loaded split test geometry and the specimen dimensions were controlled to ensure the conditions of LEFM were not violated. Data analysis was achieved by the use of corrected beam theory and experimental compliances approaches. Values of Guc were plotted against the measured crack length to yield the apparent mode II resistance curves (i.e. the mode II R-curves). These curves revealed a characteristic shape that required detailed interpretation. Uncertainties in the measured crack length values were identified as the most likely cause of the disagreement between the values of Guc deduced via corrected beam theory and experimental compliance approaches. It is suggested that these uncertainties are due to the problem of misinterpreting microcracking as the main crack growing. KEYWORDS Adhesive joints, mode II, cohesive failure, R-curve, microcracking INTRODUCTION Whilst test methods to measure the mode I fracture resistance of polymer fibre-composites [1] and structural adhesive joints [2,3] have now proceeded to full standards, the efforts to standardise a mode II method have been beset by a number of problems. Firstly, there exist a number of competing tests: e.g. the end-loaded split (ELS), the end-notched flexure (ENF), the four point end-notched flexure (4-ENF) and the stabilised end-notched flexure (S-ENF) have all been proposed and have been subjected to various inter-laboratory evaluations. However, the results of these programmes have always revealed a very large scatter in the values of Guc measured e.g. [4], and this scatter has been variously attributed to friction
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B.R.K. BLACKMAN, A.J. KINLOCHANDM. PARASCHI
effects, problems with specimen calibration, difficulty in measuring crack length and microcracking. Indeed, such problems will influence the mode II testing of both polyme • fibre-composites and adhesive joints, however, it has been far from clear which of thes'.; issues are the most significant. Early attempts to quantify the frictional effects during the mode II ELS testing of polymer fibre-composites [5] gave promising results, suggesting that friction could account for a;; much as 20% of the measured mode II fracture energy in a carbon-fibre PEEK composite and as much as 30% in a carbon-fibre epoxy composite. However, repeating these analyses for structural adhesive joints has so far been less successful. The results would suggest that whilst friction does indeed play a role in elevating the measured G\\Q values and hence the Rcurves in the ELS test, it is not the major factor responsible for the very strongly rising values of Giic seen in the present work. The results presented here provide some insight into thtnature of the mode II R-curves measured during ELS testing of structural adhesive joints and demonstrate that the fracture toughness variation calculated is consistent with the development and propagation of microcracks within the adhesive layer. EXPERIMENTAL Joint manufacture The adhesive joints tested in the present work were manufactured using 2mm thick carbon fibre-composite substrates (T300/924 from Hexcel, UK). The substrates were thoroughly dried in an oven immediately prior to bonding to remove any pre-bond moisture from the beams. The substrates were abraded and solvent wiped prior to bonding. Joints were then formed by bonding with either an aerospace epoxy-film adhesive (API26 from 3M Inc.) or with a general purpose epoxy-paste adhesive (ESPl 10 from Permabond Pic). A release film of PTFE was inserted into the bondline at one end to create a crack starter. The joints were cured according to the adhesive manufacturer's instructions. The bondline thickness was controlled during manufacture and was 0.08+0.04 mm for the epoxy-film adhesive and 0.4+0.05 mm for the epoxy-paste adhesive. The sides of the joints were machined to remove excess adhesive and white paint was applied to the joint sides to facilitate crack length measurement.
Fig. 1. The end-loaded split (ELS) test fixture and adhesive joint specimen.
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Fracture testing The joints were precracked in mode I, prior to mode II testing such that the crack grew 2 to 3 mm away from the end of the insert film. This was to improve the stability of the mode II test and create a sharp, natural crack. The specimens were then clamped in the ELS test fixture with a free length, L, of about 125mm. Tests were run in displacement control at a rate of Imm/min. The crack was monitored at the edge of the specimen using a travelling microscope with a magnification X7. This follows the recommendations of the ESIS mode II ELS test protocol for composites [7]. The crack was grown until it reached 10 mm from clamp point. The load, cross-head displacement and crack length were recorded for each increment of crack growth. The test was then stopped and final unloading was performed at 5mm/min. On final unloading, the load-displacement trace returned to the origin, confirming that no permanent plastic deformation of the substrate arms had occurred during the test. The arms of the specimen were then examined for any signs of permanent deformation, before being broken open to assess the locus of joint failure. The compliance of the test fixture was measured by clamping a very stiff calibration specimen in place of the test specimen, and loading the system up to the loads expected during the tests. The system compliance measured was IxlO'"^ mm/N. The displacement values measured for the fracture test were then corrected for system compliance effects. Some additional tests were performed using a more powerful microscope connected to a CCD camera to monitor the crack propagation. ANALYSIS The tests have been analysed to determine the mode II adhesive fracture energy, Guc, using both corrected beam theory and the experimental compliance approaches. The corrected beam theory used was that derived in [6] for the fracture of fibre-composite specimens and now embodied in the ESIS TC4 protocol for ELS testing [7]. The earlier studies on mode I loading [2, 3] have demonstrated that, provided the adhesive layer is relatively thin, it can be neglected in a global energy balance approach for the determination of G, as followed here. The analysis requires the load, P, the displacement, 5, and crack length, a, to be measured at a number of crack length increments. Also required is the beam width, b, the beam height, h and the known flexural modulus of the beam, E. This may be measured in an independent modulus test, or taken as quoted by the manufacturer if a standard grade of material is used. To correct beam theory for the effects of beam root rotation and transverse shear, a correction factor, A\\, is required where A\\ is usually determined from the mode I correction. In this scheme, A\\ =Ziih and Xu is deduced from Zvr^-^^X\ [^J- The value ofxi ^^Y be determined from a mode I test or may be calculated from the elastic properties of the substrate. Corrected beam theory (CBT) may thus be expressed as:
where F is a large displacement correction factor defined in [6]. Beam theory may also be used to eliminate the modulus in eqn. (1) and such an approach leads to a second expression for Giic, called here corrected beam theory with displacement (CBTD): . 9P5 i^ + ^II? '^^^~ 2b{a + Ajj) 3{a + Ajjf +{L + 2Ajf
^ N
(2)
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B.R.K. BLACKMAN, A J. KINLOCH AND M. PARASCHI
where L is the free length of the specimen i.e. between the load-Hne and the clamp poin^, A\=x\h and // is a correction factor to account for the presence of the bonded on end-blocks and was defined in [6]. From this procedure, the flexural modulus of the beam, Ef, may b^ expressed as: p(3(a + A / / ) ^ + ( l + 2A/)^) ^f-^^ ^^^ ;^ ^ ^ ^-A^ 2hh^5
(3)
Thus, corrected beam theory can be used to deduce the value of Ef from the mode II fracture test, and this allows an important cross-check on the results to be performed, as the value can be compared to the known, or independently measured value, E, as used in eqn (1). Also the value of £/so deduced should be independent of crack length, a. If a compliance calibration of the form C=Co+mfl^ is assumed as suggested in the ESIS TC4 protocol [7], where C is the compliance i.e. {5IP) and Co and m are constants, then G\\c may be determined from the experimental compliance method (ECM) as:
G , c - ' - ^ - F
(4)
where m is determined from the slope of a plot of C versus a^. Such a procedure allows a cross check to be made with the corrected beam theory values of Guc- The results of the ELS tests on the adhesive joints are now presented and discussed.
RESULTS & DISCUSSION All crack propagation was cohesive in the adhesive layer and was largely stable. Fig. 2 shows a typical force-displacement trace for a joint bonded with the epoxy-film adhesive. In this test, the initial precrack length, Up, was 74mm and the free length, L, was 125mm. The experimentally measured crack lengths have been indicated on Fig. 2. The crack initiation values determined via (a) deviation from initial linearity (NL), (b) visually detected (VIS) and (c) 5% offset of initial compliance (5%) are all shown. Fig. 3 shows a typical forcedisplacement trace for a joint bonded with the epoxy-paste adhesive. Here the ap=65mm and again L= 125mm. The experimentally measured values of crack length for initiation and propagation are again shown on the diagram. The data in Figs. 2 and 3 were analysed as described above to yield values of Guc as a function of measured crack length, i.e. the R-curves were computed. In addition, the back calculated values of substrate modulus were compared to the known values of the flexural modulus of the arms. The R-curves are shown in Figs. 4 and 5 for the epoxy-film and epoxypaste adhesives respectively. Each curve shows the values of Guc calculated via the three analysis approached outlined above, i.e. the CBT approach (eqn. 1), the CBTD approach (eqn. 2) and the ECM approach (eqn. 3). The general pattern was for Guc to rise strongly following crack initiation and then fmally reach a plateau of almost constant Guc- The initial apparent decrease in Guc following initiation is an artefact caused by the quite extensive apparent crack growth prior to the 5% offset initiation value. As the 5% initiation value of Guc was plotted
On the Mode II Loading ofAdhesive Joints
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10
15 20 25 30 35 Displacement [mm] Fig. 2 Typical force-displacement trace for a CFRP joint bonded with the epoxy-film adhesive. (Crack length, a, values in mm.) 400
20 30 Displacement [mm]
50
Fig. 3 Typical force-displacement trace for a CFRP joint bonded with the epoxy-paste adhesive. (Craclc length, a, values in mm.)
B.R.K. BLACKMAN, A J. KINWCHANDM. PARASCHI
298 4000 3500 3000 _
2500 y 2000
O
1500 1000
o n e (CBT) ^— GIIC (CBTD)
500
»— o n e (ECM) I
0 70
80
I
90 100 Measured crack length [mm]
I
I
I
I
I
110
L
120
Fig. 4 Giic versus measured a for the CFRP joints bonded with the epoxy-film adhesive. 7000 6000
5000
I
4000
^
3000
2000
-^— GIIC (CBT) -^^— GIIC (CBTD)
1000
-<— GIIC (ECM) 0
60
70
80 90 Measured crack length [mm]
100
110
Fig. 5 GIIC versus measured a for the CFRP joints bonded with the epoxy-paste adhesive.
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at the initial crack length, ^p, rather than at the visually assessed crack length at this instant, there is an apparent decrease in Gnc following this point. It is seen that the different analysis schemes return somewhat different R-curves for each adhesive, and the trend was that the highest values were deduced by using the CBT analysis and the lowest by the ECM analysis, with the CBTD analysis giving results that lie inbetween. 170
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epoxy-film adhesive epoxy-paste adhesive 1
1
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^ 120
Measured crack length [mm] Fig. 6. Values of back-calculated modulus for the joints as a function of measured crack length. (Note that the known value of theflexuralmodulus, E, of the substrate was 126GPa) The accuracy of the CBT and CBTD equations can be assessed by determining the values of the back-calculated modulus, Ef, of the substrate arms. These values are shown in Fig. 6 for both sets of data. It is clear from these results that the back-calculated values of Ef are about 19% higher than the known values for the substrate when bonding with the epoxy-film adhesive and about 11% higher than the known values when bonding with the epoxy-paste adhesive. This discrepancy is most likely to be the result of the uncertainties in measuring the crack length. Fracture in mode II occurs by the development and coalescence of microcracks [9, 10] and microcracking was observed and photographed experimentally in the present work [11]. Fig. 7 shows the microcracking observed at the side of the specimen for a joint bonded with the epoxy-film adhesive. The top photograph shows this at a magnification of X80 and the lower photograph at XI80. For this joint, the cracking extends across the entire height of the adhesive layer. Clearly, measuring crack length with a high degree of certainty when microcracking is occurring is a difficult task and one which is yet to be addressed in the mode II test protocols. Whilst it would be obviously desirable to have a more accurate method to measure crack lengths experimentally in mode II, such techniques are currently not readily
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B.R.K. BLACKMAN, A J. KINLOCHANDM. PARASCHI
w h ' I loaded t n : . " !in: ;shear. ! ! ! ''^''^ ^^"^^^ - " - * - " - - d e I, they would be very unreliab] t when
will also be subject to thisTnc'ertrintv
H
^
expressions requiring this parameter
determine an e f f c t o a k S T v i a t r ' ' ' ' ""7"'"^ " " " " ^ ^ " ' ^ '^^^ ^' "^«d ''^ iv.iicv.uvc trdCK lengm, ae, via the measured comnliance valn<- ^^nri ^^r, /a\ be rearranged to give an effective crack length thus: ^^^P^^^"^^ ^^^^e and eqn (3) may
(b)
if'6i)lri|||Hl
Substrate
Fig. 7. Photographs of microcracking in the adhesive layer for a joint bonded film adhesive. Magnification: (a) X80 (b) X180 m ''Jomt Donded with the epoxye vertical black lines in (a) are drawn 1mm apart). ' ^
S_ Ibh'E P N
{L + lA^f
where Ai-zih and Au=Zuh hence a value for the effective crack lenath .
(5) ..^ u ^ .
•
.
On the Mode II Loading ofAdhesive Joints
301
implication is that the uncertainties in measuring crack length are now unimportant because the effective crack length, QQ, is calculated. Thus, if we calculate Ue on a point-by-point basis, then an insight into the likely measured crack length uncertainties can be obtained. By following this procedure, the difference between the effective crack length, ag, and the measured crack length, a, can be determined, and expressed as a percentage for each value of the measured crack length. These data are shown in Fig. 8 for four repeat specimens bonded with the epoxy-film adhesive. These values are deduced from {(Ue -a)/ae)xlOO%. \
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r
^
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1
1
,
100
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Measured crack length [mm] Fig. 8. Discrepancy between the effective and measured crack lengths (expressed as a %) for joints bonded with the epoxy-film adhesive plotted as a function of measured crack length. These data suggest that the measured crack length values, a, are on average between 10% and 20% greater than the effective crack length values, Qe, calculated from the compliance. When these more reliable crack length values are used in the corrected beam theory analysis, then a much better agreement with the ECM analysis method is observed. This is shown in Fig. 9 for a joint bonded with the epoxy-paste adhesive (Fig. 9 is plotted from the same test as used for Fig. 5). However, the results still indicate a strongly rising R-curve effect as the microcracking develops and then a plateau to this curve, presumably after the microcracking reaches a steady-state condition. The values of G\\c for initiation (via the NL definition) and propagation (via the plateau value) for both adhesives have been compared to corresponding values measured in mode I, i.e. from double cantilever beam tests, and these results are shown in Table 1. Table I summarises the results for a large number of repeat tests for each joint type [11]. The results show that, for mode I, values of G\c for crack initiation are very similar to the G\c values for propagation, i.e. very flat R-curves are measured in mode I for both adhesive joints. However, for mode II, crack initiation occurs at a similar value of GQ as for mode I, but in mode II a very strongly rising R-curve was observed, with the plateau value of G\\c being significantly higher than the initiation value. For the joints bonded with the epoxy-film
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B.R.K. BLACKMAN, A J. KINLOCHANDM. PARASCHI
adhesive, the plateau value of Guc was about two and a half times higher than the initiation value and for the joints bonded with the epoxy-paste adhesive the plateau value of Guc was about five times higher than the initiation. 7000
' I ' ' ' • I ' ' ' ' I ' ' ' ' I ' ' ' ' I ' ' ' ' I ' ' ' ' I '
- « — GIIC (CBT, but with a values used in place of a) - e — GIIC (ECM)
6000
5000
^S
4000
^^
3000
2000
1000
60
65
70
75
80
85
90
95
100
Measured crack length [mm] Fig. 9 Giic versus measured a for the CFRP joints bonded with the epoxy-paste adhesive. (Values of Guc deduced via eqn 4 (ECM) and via eqn 2 (CBTD) with the measured crack length, a, replaced with the effective crack length, a^.)
The elevation of the R-curve may depend entirely on the increased fracture surface area generated when crack propagation is via the initiation and growth of microcracks formed at 45 degrees to the original crack plane. If the microcracks extend across the entire height of the adhesive layer (as was observed in Fig. 7 for the joints bonded with the epoxy-film adhesive) then the enhancement in fracture surface area for a 45 degree microcrack can be approximated hy42{hid) where h is the bondline thickness and d is the spacing between microcracks. For the epoxy-film adhesive, /z=0.08mm and the microcrack spacing can bo measured from the photographs to be c/=0.047mm. Hence, the enhancement in surface area for this case is 2.4 times which is very close to the 2.5 times enhancement in Guc observed. Photographs for the epoxy-paste adhesive are not currently available however, it is obvious that the thicker bondlines used for these joints (/z=0.4mm) would lead to a greater enhancement in the fracture surface area and this is in agreement with the steeper R-curves measured for these joints. Of course, more detailed photographs of the development and propagation of the microcracks in both joints are desirable to more fully understand this phenomenon.
On the Mode 11 Loading of Adhesive Joints
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Table 1. Comparison of G\c and G\\c values at initiation and for propagation in test joints tested. Mode I (DCB) Mode II (ELS) Joint Gic(init)max/5% Giic (init) NL GIIC (Plateau) Gic (Prop) 1449+113 1488+156 CFRP/AF126 3428+758 1351±481 903+74 945+28 CFRP/ESPllO 4119+577 1 755±301 Note: Cic values deduced via corrected beam theory [2,3]5 G\\c values deduced via corrected beam theory using effective crack lengths, Ug.
CONCLUSIONS Adhesive joints were manufactured using CFRP substrates bonded with either an epoxy-film or an epoxy-paste adhesive. These were tested in mode II using the ELS test geometry. Values of Gnc were deduced using two forms of corrected beam theory and an experimental compliance approach. Back-calculated values of substrate modulus were also deduced from the mode II fracture tests using the corrected beam theory. Substantial crack growth was observed prior to the maximum load point in the ELS tests. The R-curves showed strong rising effects following crack initiation until an almost constant plateau value of Gnc was obtained. The agreement between the different analysis schemes was quite poor, with the CRT yielding the highest values and the ECM yielding the lowest values. In addition, the values of the back-calculated substrate modulus were between 10-20% higher than the known values. Photographs of the specimen side revealed extensive microcracking and this made it very difficult to accurately determine the crack length by visual techniques. Crack length values were also determined via compliance measurements and this approach indicated that the measured crack lengths were typically 10-20% greater than the effective values via eqn (5). The use of effective crack length values in the analysis improved the accuracy and led to substantially better agreement between the corrected beam theory and experimental compliance approaches, as would be expected. However, even with the more accurate values of crack length, substantial rising R-curves were recorded for all the joints. The values at crack initiation and from the plateau were compared to the mode I values of Gic- Whilst crack initiation occurs at approximately the same value of Gc in the joints for both mode I and mode II, the propagation values are substantially greater in mode II than mode I. It is suggested that the extra fracture surface area generated by microcracking ahead of the main crack in the mode II ELS tests is the main cause of the strongly rising R-curves shown here.
ACKNOWLEDGEMENTS We wish to thank the Engineering and Physical Sciences Research Council (EPSRC) for an Advanced Research Fellowship (AF/992781) and a Platform Grant, and the National Physical Laboratory (NPL) for funding the PhD. studentship of Marion Paraschi. Also, we wish to thank Professor J.G. Williams for valuable discussions on the ideas presented here.
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REFERENCES
1. 2.
3.
4.
5. 6.
7.
8. 9.
10. 11.
ISO, Standard test method for mode I interlaminar fracture toughness, Gjc, of unidirectional fibre-reinforced polymer matrix composites. ISO 15024: 2001. Blackman, B.R.K., H. Hadavinia, AJ. Kinloch, M. Paraschi and J.G. Williams, The calculation of adhesive fracture energies in mode I: revisiting the tapered double cantilever beam (TDCB) test. Engineering Fracture Mechanics 2003. 70:p. 233-248. BSI, Determination of the mode I adhesive fracture energy, Gjc, of structural adhesives using the double cantilever beam (DCB) and tapered double cantilever beam (TDCB) specimens. 2001. BS 7991. Davies, P., G.D. Sims, B.R.K. Blackman, A.J. Brunner, K. Kageyama, M. Hojo, K. Tanaka, G.B. Murri, C.Q. Rousseau, B. Gieseke, and R. Martin, Comparison of test configurations for determination of mode II interlaminar fracture toughness results from international collaborative test programme. Plastics, Rubber and Composites, 1999. 28(9): p. 432-437. Blackman, B.R.K. and J.G. Williams. On the mode II testing of carbon-fibre polymer composites, in ECF12 Fracture from Defects. 1998. Sheffield, UK: EMAS publishing. Hashemi, S., A.J. Kinloch, and J.G. Williams, The analysis of interlaminar fracture in uniaxial fibre-polymer composites. Proceeding of the Royal Society London, 1990. A427: p. 173-199. Davies, P., B.R.K. Blackman, and A.J. Brunner, Mode II delamination, in Fracture mechanics testing methods for polymers adhesives and composites, D.R. Moore, A. Pavan, and J.G. Williams, Editors. 2001, Elsevier: Amsterdam, London, New York. p. 307-334. Wang, Y. and J.G. Williams, Corrections for mode IIfracture toughness specimens of composite materials. Composites Science and Technology, 1992. 43: p. 251-256. O'Brien, T.K., Composite interlaminar shear fracture toughness, Gnc-' Shear measurement or sheer myth? in Composite Materials: Fatigue and Fracture 1. 1998 ASTM STP 1330 p.3-18. Lee, S.M., Mode II delamination failure mechanisms of polymer matrix composites. Journal of Materials Science, 1997. 32: p. 1287-1295. Paraschi, M., A fracture mechanics approach to the failure of adhesive joints, PhD thesis. Department of Mechanical Engineering. 2002, Imperial College, University of London: London.
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ON THE MODE II LOADING OF ADHESIVE JOINTS
B.R.K. BLACKMAN, AJ. KINLOCH & M. PARASCHI Department of Mechanical Engineering Imperial College London Exhibition Road London SW7 2BX. UK.
ABSTRACT This paper reports the results of research studies on measuring the mode II fracture toughness, Giic, of structural adhesive joints via a Linear Elastic Fracture Mechanics (LEFM) test method. Adhesive joints were manufactured using carbon-fibre reinforced plastic substrates and these were bonded with one of two commercial structural epoxy adhesives. Mode II loading was achieved using the end-loaded split test geometry and the specimen dimensions were controlled to ensure the conditions of LEFM were not violated. Data analysis was achieved by the use of corrected beam theory and experimental compliances approaches. Values of Guc were plotted against the measured crack length to yield the apparent mode II resistance curves (i.e. the mode II R-curves). These curves revealed a characteristic shape that required detailed interpretation. Uncertainties in the measured crack length values were identified as the most likely cause of the disagreement between the values of Guc deduced via corrected beam theory and experimental compliance approaches. It is suggested that these uncertainties are due to the problem of misinterpreting microcracking as the main crack growing. KEYWORDS Adhesive joints, mode II, cohesive failure, R-curve, microcracking INTRODUCTION Whilst test methods to measure the mode I fracture resistance of polymer fibre-composites [1] and structural adhesive joints [2,3] have now proceeded to full standards, the efforts to standardise a mode II method have been beset by a number of problems. Firstly, there exist a number of competing tests: e.g. the end-loaded split (ELS), the end-notched flexure (ENF), the four point end-notched flexure (4-ENF) and the stabilised end-notched flexure (S-ENF) have all been proposed and have been subjected to various inter-laboratory evaluations. However, the results of these programmes have always revealed a very large scatter in the values of Guc measured e.g. [4], and this scatter has been variously attributed to friction
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B.R.K. BLACKMAN, A.J. KINLOCHANDM. PARASCHI
effects, problems with specimen calibration, difficulty in measuring crack length and microcracking. Indeed, such problems will influence the mode II testing of both polyme • fibre-composites and adhesive joints, however, it has been far from clear which of thes'.; issues are the most significant. Early attempts to quantify the frictional effects during the mode II ELS testing of polymer fibre-composites [5] gave promising results, suggesting that friction could account for a;; much as 20% of the measured mode II fracture energy in a carbon-fibre PEEK composite and as much as 30% in a carbon-fibre epoxy composite. However, repeating these analyses for structural adhesive joints has so far been less successful. The results would suggest that whilst friction does indeed play a role in elevating the measured G\\Q values and hence the Rcurves in the ELS test, it is not the major factor responsible for the very strongly rising values of Giic seen in the present work. The results presented here provide some insight into thtnature of the mode II R-curves measured during ELS testing of structural adhesive joints and demonstrate that the fracture toughness variation calculated is consistent with the development and propagation of microcracks within the adhesive layer. EXPERIMENTAL Joint manufacture The adhesive joints tested in the present work were manufactured using 2mm thick carbon fibre-composite substrates (T300/924 from Hexcel, UK). The substrates were thoroughly dried in an oven immediately prior to bonding to remove any pre-bond moisture from the beams. The substrates were abraded and solvent wiped prior to bonding. Joints were then formed by bonding with either an aerospace epoxy-film adhesive (API26 from 3M Inc.) or with a general purpose epoxy-paste adhesive (ESPl 10 from Permabond Pic). A release film of PTFE was inserted into the bondline at one end to create a crack starter. The joints were cured according to the adhesive manufacturer's instructions. The bondline thickness was controlled during manufacture and was 0.08+0.04 mm for the epoxy-film adhesive and 0.4+0.05 mm for the epoxy-paste adhesive. The sides of the joints were machined to remove excess adhesive and white paint was applied to the joint sides to facilitate crack length measurement.
Fig. 1. The end-loaded split (ELS) test fixture and adhesive joint specimen.
On the Mode II Loading ofAdhesive Joints
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Fracture testing The joints were precracked in mode I, prior to mode II testing such that the crack grew 2 to 3 mm away from the end of the insert film. This was to improve the stability of the mode II test and create a sharp, natural crack. The specimens were then clamped in the ELS test fixture with a free length, L, of about 125mm. Tests were run in displacement control at a rate of Imm/min. The crack was monitored at the edge of the specimen using a travelling microscope with a magnification X7. This follows the recommendations of the ESIS mode II ELS test protocol for composites [7]. The crack was grown until it reached 10 mm from clamp point. The load, cross-head displacement and crack length were recorded for each increment of crack growth. The test was then stopped and final unloading was performed at 5mm/min. On final unloading, the load-displacement trace returned to the origin, confirming that no permanent plastic deformation of the substrate arms had occurred during the test. The arms of the specimen were then examined for any signs of permanent deformation, before being broken open to assess the locus of joint failure. The compliance of the test fixture was measured by clamping a very stiff calibration specimen in place of the test specimen, and loading the system up to the loads expected during the tests. The system compliance measured was IxlO'"^ mm/N. The displacement values measured for the fracture test were then corrected for system compliance effects. Some additional tests were performed using a more powerful microscope connected to a CCD camera to monitor the crack propagation. ANALYSIS The tests have been analysed to determine the mode II adhesive fracture energy, Guc, using both corrected beam theory and the experimental compliance approaches. The corrected beam theory used was that derived in [6] for the fracture of fibre-composite specimens and now embodied in the ESIS TC4 protocol for ELS testing [7]. The earlier studies on mode I loading [2, 3] have demonstrated that, provided the adhesive layer is relatively thin, it can be neglected in a global energy balance approach for the determination of G, as followed here. The analysis requires the load, P, the displacement, 5, and crack length, a, to be measured at a number of crack length increments. Also required is the beam width, b, the beam height, h and the known flexural modulus of the beam, E. This may be measured in an independent modulus test, or taken as quoted by the manufacturer if a standard grade of material is used. To correct beam theory for the effects of beam root rotation and transverse shear, a correction factor, A\\, is required where A\\ is usually determined from the mode I correction. In this scheme, A\\ =Ziih and Xu is deduced from Zvr^-^^X\ [^J- The value ofxi ^^Y be determined from a mode I test or may be calculated from the elastic properties of the substrate. Corrected beam theory (CBT) may thus be expressed as:
where F is a large displacement correction factor defined in [6]. Beam theory may also be used to eliminate the modulus in eqn. (1) and such an approach leads to a second expression for Giic, called here corrected beam theory with displacement (CBTD): . 9P5 i^ + ^II? '^^^~ 2b{a + Ajj) 3{a + Ajjf +{L + 2Ajf
^ N
(2)
296
B.R.K. BLACKMAN, A J. KINLOCH AND M. PARASCHI
where L is the free length of the specimen i.e. between the load-Hne and the clamp poin^, A\=x\h and // is a correction factor to account for the presence of the bonded on end-blocks and was defined in [6]. From this procedure, the flexural modulus of the beam, Ef, may b^ expressed as: p(3(a + A / / ) ^ + ( l + 2A/)^) ^f-^^ ^^^ ;^ ^ ^ ^-A^ 2hh^5
(3)
Thus, corrected beam theory can be used to deduce the value of Ef from the mode II fracture test, and this allows an important cross-check on the results to be performed, as the value can be compared to the known, or independently measured value, E, as used in eqn (1). Also the value of £/so deduced should be independent of crack length, a. If a compliance calibration of the form C=Co+mfl^ is assumed as suggested in the ESIS TC4 protocol [7], where C is the compliance i.e. {5IP) and Co and m are constants, then G\\c may be determined from the experimental compliance method (ECM) as:
G , c - ' - ^ - F
(4)
where m is determined from the slope of a plot of C versus a^. Such a procedure allows a cross check to be made with the corrected beam theory values of Guc- The results of the ELS tests on the adhesive joints are now presented and discussed.
RESULTS & DISCUSSION All crack propagation was cohesive in the adhesive layer and was largely stable. Fig. 2 shows a typical force-displacement trace for a joint bonded with the epoxy-film adhesive. In this test, the initial precrack length, Up, was 74mm and the free length, L, was 125mm. The experimentally measured crack lengths have been indicated on Fig. 2. The crack initiation values determined via (a) deviation from initial linearity (NL), (b) visually detected (VIS) and (c) 5% offset of initial compliance (5%) are all shown. Fig. 3 shows a typical forcedisplacement trace for a joint bonded with the epoxy-paste adhesive. Here the ap=65mm and again L= 125mm. The experimentally measured values of crack length for initiation and propagation are again shown on the diagram. The data in Figs. 2 and 3 were analysed as described above to yield values of Guc as a function of measured crack length, i.e. the R-curves were computed. In addition, the back calculated values of substrate modulus were compared to the known values of the flexural modulus of the arms. The R-curves are shown in Figs. 4 and 5 for the epoxy-film and epoxypaste adhesives respectively. Each curve shows the values of Guc calculated via the three analysis approached outlined above, i.e. the CBT approach (eqn. 1), the CBTD approach (eqn. 2) and the ECM approach (eqn. 3). The general pattern was for Guc to rise strongly following crack initiation and then fmally reach a plateau of almost constant Guc- The initial apparent decrease in Guc following initiation is an artefact caused by the quite extensive apparent crack growth prior to the 5% offset initiation value. As the 5% initiation value of Guc was plotted
On the Mode II Loading ofAdhesive Joints
297
10
15 20 25 30 35 Displacement [mm] Fig. 2 Typical force-displacement trace for a CFRP joint bonded with the epoxy-film adhesive. (Crack length, a, values in mm.) 400
20 30 Displacement [mm]
50
Fig. 3 Typical force-displacement trace for a CFRP joint bonded with the epoxy-paste adhesive. (Craclc length, a, values in mm.)
B.R.K. BLACKMAN, A J. KINWCHANDM. PARASCHI
298 4000 3500 3000 _
2500 y 2000
O
1500 1000
o n e (CBT) ^— GIIC (CBTD)
500
»— o n e (ECM) I
0 70
80
I
90 100 Measured crack length [mm]
I
I
I
I
I
110
L
120
Fig. 4 Giic versus measured a for the CFRP joints bonded with the epoxy-film adhesive. 7000 6000
5000
I
4000
^
3000
2000
-^— GIIC (CBT) -^^— GIIC (CBTD)
1000
-<— GIIC (ECM) 0
60
70
80 90 Measured crack length [mm]
100
110
Fig. 5 GIIC versus measured a for the CFRP joints bonded with the epoxy-paste adhesive.
On the Mode II Loading ofAdhesive Joints
299
at the initial crack length, ^p, rather than at the visually assessed crack length at this instant, there is an apparent decrease in Gnc following this point. It is seen that the different analysis schemes return somewhat different R-curves for each adhesive, and the trend was that the highest values were deduced by using the CBT analysis and the lowest by the ECM analysis, with the CBTD analysis giving results that lie inbetween. 170
'
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1 1 ' —1
1
1
1 1
-
160
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150
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•
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•
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0
140
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\^
130
120
0
o
0
-
-
E=126GPa
-
• o
110
100
-
0 0
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^ 60
1
i
1
1
70
1
1
1
1
1 1_j
80
1
1
1
90
1
1
1
epoxy-film adhesive epoxy-paste adhesive 1
1
1
100
1
1
1
1
110
1
1
1
^ 120
Measured crack length [mm] Fig. 6. Values of back-calculated modulus for the joints as a function of measured crack length. (Note that the known value of theflexuralmodulus, E, of the substrate was 126GPa) The accuracy of the CBT and CBTD equations can be assessed by determining the values of the back-calculated modulus, Ef, of the substrate arms. These values are shown in Fig. 6 for both sets of data. It is clear from these results that the back-calculated values of Ef are about 19% higher than the known values for the substrate when bonding with the epoxy-film adhesive and about 11% higher than the known values when bonding with the epoxy-paste adhesive. This discrepancy is most likely to be the result of the uncertainties in measuring the crack length. Fracture in mode II occurs by the development and coalescence of microcracks [9, 10] and microcracking was observed and photographed experimentally in the present work [11]. Fig. 7 shows the microcracking observed at the side of the specimen for a joint bonded with the epoxy-film adhesive. The top photograph shows this at a magnification of X80 and the lower photograph at XI80. For this joint, the cracking extends across the entire height of the adhesive layer. Clearly, measuring crack length with a high degree of certainty when microcracking is occurring is a difficult task and one which is yet to be addressed in the mode II test protocols. Whilst it would be obviously desirable to have a more accurate method to measure crack lengths experimentally in mode II, such techniques are currently not readily
300
B.R.K. BLACKMAN, A J. KINLOCHANDM. PARASCHI
w h ' I loaded t n : . " !in: ;shear. ! ! ! ''^''^ ^^"^^^ - " - * - " - - d e I, they would be very unreliab] t when
will also be subject to thisTnc'ertrintv
H
^
expressions requiring this parameter
determine an e f f c t o a k S T v i a t r ' ' ' ' ""7"'"^ " " " " ^ ^ " ' ^ '^^^ ^' "^«d ''^ iv.iicv.uvc trdCK lengm, ae, via the measured comnliance valn<- ^^nri ^^r, /a\ be rearranged to give an effective crack length thus: ^^^P^^^"^^ ^^^^e and eqn (3) may
(b)
if'6i)lri|||Hl
Substrate
Fig. 7. Photographs of microcracking in the adhesive layer for a joint bonded film adhesive. Magnification: (a) X80 (b) X180 m ''Jomt Donded with the epoxye vertical black lines in (a) are drawn 1mm apart). ' ^
S_ Ibh'E P N
{L + lA^f
where Ai-zih and Au=Zuh hence a value for the effective crack lenath .
(5) ..^ u ^ .
•
.
On the Mode II Loading ofAdhesive Joints
301
implication is that the uncertainties in measuring crack length are now unimportant because the effective crack length, QQ, is calculated. Thus, if we calculate Ue on a point-by-point basis, then an insight into the likely measured crack length uncertainties can be obtained. By following this procedure, the difference between the effective crack length, ag, and the measured crack length, a, can be determined, and expressed as a percentage for each value of the measured crack length. These data are shown in Fig. 8 for four repeat specimens bonded with the epoxy-film adhesive. These values are deduced from {(Ue -a)/ae)xlOO%. \
^1
r
^
\
r
-n—1
^ \ ^
0
•
^—^—^—
•
Specimen 1
O
Specimen 2
•
Specimen 3
D
Specimen 4
\
• •
-10
O •
•
;
n
•
n
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•
0
0 •
-20
•
• •
•
•
0
-
D
• 1
-25 70
1
.
1
1
90
,
1
1
,
100
110
120
Measured crack length [mm] Fig. 8. Discrepancy between the effective and measured crack lengths (expressed as a %) for joints bonded with the epoxy-film adhesive plotted as a function of measured crack length. These data suggest that the measured crack length values, a, are on average between 10% and 20% greater than the effective crack length values, Qe, calculated from the compliance. When these more reliable crack length values are used in the corrected beam theory analysis, then a much better agreement with the ECM analysis method is observed. This is shown in Fig. 9 for a joint bonded with the epoxy-paste adhesive (Fig. 9 is plotted from the same test as used for Fig. 5). However, the results still indicate a strongly rising R-curve effect as the microcracking develops and then a plateau to this curve, presumably after the microcracking reaches a steady-state condition. The values of G\\c for initiation (via the NL definition) and propagation (via the plateau value) for both adhesives have been compared to corresponding values measured in mode I, i.e. from double cantilever beam tests, and these results are shown in Table 1. Table I summarises the results for a large number of repeat tests for each joint type [11]. The results show that, for mode I, values of G\c for crack initiation are very similar to the G\c values for propagation, i.e. very flat R-curves are measured in mode I for both adhesive joints. However, for mode II, crack initiation occurs at a similar value of GQ as for mode I, but in mode II a very strongly rising R-curve was observed, with the plateau value of G\\c being significantly higher than the initiation value. For the joints bonded with the epoxy-film
302
B.R.K. BLACKMAN, A J. KINLOCHANDM. PARASCHI
adhesive, the plateau value of Guc was about two and a half times higher than the initiation value and for the joints bonded with the epoxy-paste adhesive the plateau value of Guc was about five times higher than the initiation. 7000
' I ' ' ' • I ' ' ' ' I ' ' ' ' I ' ' ' ' I ' ' ' ' I ' ' ' ' I '
- « — GIIC (CBT, but with a values used in place of a) - e — GIIC (ECM)
6000
5000
^S
4000
^^
3000
2000
1000
60
65
70
75
80
85
90
95
100
Measured crack length [mm] Fig. 9 Giic versus measured a for the CFRP joints bonded with the epoxy-paste adhesive. (Values of Guc deduced via eqn 4 (ECM) and via eqn 2 (CBTD) with the measured crack length, a, replaced with the effective crack length, a^.)
The elevation of the R-curve may depend entirely on the increased fracture surface area generated when crack propagation is via the initiation and growth of microcracks formed at 45 degrees to the original crack plane. If the microcracks extend across the entire height of the adhesive layer (as was observed in Fig. 7 for the joints bonded with the epoxy-film adhesive) then the enhancement in fracture surface area for a 45 degree microcrack can be approximated hy42{hid) where h is the bondline thickness and d is the spacing between microcracks. For the epoxy-film adhesive, /z=0.08mm and the microcrack spacing can bo measured from the photographs to be c/=0.047mm. Hence, the enhancement in surface area for this case is 2.4 times which is very close to the 2.5 times enhancement in Guc observed. Photographs for the epoxy-paste adhesive are not currently available however, it is obvious that the thicker bondlines used for these joints (/z=0.4mm) would lead to a greater enhancement in the fracture surface area and this is in agreement with the steeper R-curves measured for these joints. Of course, more detailed photographs of the development and propagation of the microcracks in both joints are desirable to more fully understand this phenomenon.
On the Mode 11 Loading of Adhesive Joints
303
Table 1. Comparison of G\c and G\\c values at initiation and for propagation in test joints tested. Mode I (DCB) Mode II (ELS) Joint Gic(init)max/5% Giic (init) NL GIIC (Plateau) Gic (Prop) 1449+113 1488+156 CFRP/AF126 3428+758 1351±481 903+74 945+28 CFRP/ESPllO 4119+577 1 755±301 Note: Cic values deduced via corrected beam theory [2,3]5 G\\c values deduced via corrected beam theory using effective crack lengths, Ug.
CONCLUSIONS Adhesive joints were manufactured using CFRP substrates bonded with either an epoxy-film or an epoxy-paste adhesive. These were tested in mode II using the ELS test geometry. Values of Gnc were deduced using two forms of corrected beam theory and an experimental compliance approach. Back-calculated values of substrate modulus were also deduced from the mode II fracture tests using the corrected beam theory. Substantial crack growth was observed prior to the maximum load point in the ELS tests. The R-curves showed strong rising effects following crack initiation until an almost constant plateau value of Gnc was obtained. The agreement between the different analysis schemes was quite poor, with the CRT yielding the highest values and the ECM yielding the lowest values. In addition, the values of the back-calculated substrate modulus were between 10-20% higher than the known values. Photographs of the specimen side revealed extensive microcracking and this made it very difficult to accurately determine the crack length by visual techniques. Crack length values were also determined via compliance measurements and this approach indicated that the measured crack lengths were typically 10-20% greater than the effective values via eqn (5). The use of effective crack length values in the analysis improved the accuracy and led to substantially better agreement between the corrected beam theory and experimental compliance approaches, as would be expected. However, even with the more accurate values of crack length, substantial rising R-curves were recorded for all the joints. The values at crack initiation and from the plateau were compared to the mode I values of Gic- Whilst crack initiation occurs at approximately the same value of Gc in the joints for both mode I and mode II, the propagation values are substantially greater in mode II than mode I. It is suggested that the extra fracture surface area generated by microcracking ahead of the main crack in the mode II ELS tests is the main cause of the strongly rising R-curves shown here.
ACKNOWLEDGEMENTS We wish to thank the Engineering and Physical Sciences Research Council (EPSRC) for an Advanced Research Fellowship (AF/992781) and a Platform Grant, and the National Physical Laboratory (NPL) for funding the PhD. studentship of Marion Paraschi. Also, we wish to thank Professor J.G. Williams for valuable discussions on the ideas presented here.
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B.R.K. BLACKMAN, A J. KINLOCH AND M. PARASCHI
REFERENCES
1. 2.
3.
4.
5. 6.
7.
8. 9.
10. 11.
ISO, Standard test method for mode I interlaminar fracture toughness, Gjc, of unidirectional fibre-reinforced polymer matrix composites. ISO 15024: 2001. Blackman, B.R.K., H. Hadavinia, AJ. Kinloch, M. Paraschi and J.G. Williams, The calculation of adhesive fracture energies in mode I: revisiting the tapered double cantilever beam (TDCB) test. Engineering Fracture Mechanics 2003. 70:p. 233-248. BSI, Determination of the mode I adhesive fracture energy, Gjc, of structural adhesives using the double cantilever beam (DCB) and tapered double cantilever beam (TDCB) specimens. 2001. BS 7991. Davies, P., G.D. Sims, B.R.K. Blackman, A.J. Brunner, K. Kageyama, M. Hojo, K. Tanaka, G.B. Murri, C.Q. Rousseau, B. Gieseke, and R. Martin, Comparison of test configurations for determination of mode II interlaminar fracture toughness results from international collaborative test programme. Plastics, Rubber and Composites, 1999. 28(9): p. 432-437. Blackman, B.R.K. and J.G. Williams. On the mode II testing of carbon-fibre polymer composites, in ECF12 Fracture from Defects. 1998. Sheffield, UK: EMAS publishing. Hashemi, S., A.J. Kinloch, and J.G. Williams, The analysis of interlaminar fracture in uniaxial fibre-polymer composites. Proceeding of the Royal Society London, 1990. A427: p. 173-199. Davies, P., B.R.K. Blackman, and A.J. Brunner, Mode II delamination, in Fracture mechanics testing methods for polymers adhesives and composites, D.R. Moore, A. Pavan, and J.G. Williams, Editors. 2001, Elsevier: Amsterdam, London, New York. p. 307-334. Wang, Y. and J.G. Williams, Corrections for mode IIfracture toughness specimens of composite materials. Composites Science and Technology, 1992. 43: p. 251-256. O'Brien, T.K., Composite interlaminar shear fracture toughness, Gnc-' Shear measurement or sheer myth? in Composite Materials: Fatigue and Fracture 1. 1998 ASTM STP 1330 p.3-18. Lee, S.M., Mode II delamination failure mechanisms of polymer matrix composites. Journal of Materials Science, 1997. 32: p. 1287-1295. Paraschi, M., A fracture mechanics approach to the failure of adhesive joints, PhD thesis. Department of Mechanical Engineering. 2002, Imperial College, University of London: London.